The various publications that are cited below are incorporated by reference herein.
Methods have been developed for growing NWs and carbon nanotubes (NTs) whose diameters are on the order of a few nanometers (a few molecular diameters). Reference in this regard may be had to: Cees Dekker, Carbon nanotubes as molecular quantum wires, Physics Today, pages 22-28, May 1999; Y. Cui, L. Lauhon, M. Gudiksen, J. Wang, and C. M. Lieber, Diameter-controlled synthesis of single crystal silicon nanowires, Applied Physics Letters, 78(15):2214-2216, 2001; A. M. Morales and C. M. Lieber, A laser ablation method for synthesis of crystalline semiconductor nanowires, Science, 279:208-211, 1998; Nicholas A. Melosh, Akram Boukai, Frederic Diana, Brian Gerardot, Antonio Badolato, Pierre M. Petroff, and James R. Heath, Ultrahigh-density nanowire lattices and circuits, Science, 300:112-115, Apr. 4, 2003; and B. Johnston-Halperin, R. Beckman, Y. Luo, N. Melosh, J. Green, and J. R. Heath, Fabrication of conducting silicon nanowire arrays, J. Applied Physics Letters, 96(10):5921-5923, 2004. Methods have also been developed to assemble NWs into nanoarrays, crossbars containing two orthogonal sets of parallel wires on either side of a molecular layer. Reference in this regard can be made to: Nicholas A. Melosh, Akram Boukai, Frederic Diana, Brian Gerardot, Antonio Badolato, Pierre M. Petroff, and James R. Heath, Ultrahigh-density nanowire lattices and circuits, Science, 300:112-115, Apr. 4, 2003; P. J. Kuekes, R. S. Williams, and J. R. Heath, Molecular wire crossbar memory, U.S. Pat. No. 6,128,214, Oct. 3, 2000; Yong Chen, Gun-Young Jung, Doublas A. A. Ohlberg, Xuenia Li, Duncan R. Stewart, Jon O. Jeppeson, Kent A. Nielson, J. Fraser Stoddart, and R. Stanley Williams, Nanoscale molecular-switch crossbar circuits, Nanotechnology, 14:462-468, 2003; Dongmok Whang, Song Jin, and Charles M. Lieber, Nanolithography using hierarchically assembled nanowire masks, Nano Letters, 3(7):951-954, 2003; Zhaohui Zhong, Deli Wang, Yi Cui, Marc W. Bockrath, and Charles M. Lieber, Nanowire crossbar arrays as address decoders for integrated nanosystems, Science, 302:1377-1379, 2003; Y. Huang, X. Duan, Q. Wei, and C. M. Lieber, Directed assembly of one-dimensional nano structures into functional networks, Science, 291:630-633, 2001; and Franklin Kim, Serena Kwan, Jennifer Akana, and Peidong Yang, Langmuir-Blodgett nanorod assembly, Journal of the American Chemical Society, 123(18):4360-4361, 2001. The molecules in the molecular layer are chosen so that under the application of large positive and negative electric fields they change their conductivity. Reference in this regard can be had to: Charles P. Collier, Gunter Mattersteig, Eric W. Wong, Yi Luo, Kristen Beverly, José Sampaio, Francisco Raymo, J. Fraser Stoddart, and James R. Heath, A [2]catenate-based solid state electronically reconfigurable switch, Science, 290:1172-1175, 2000; C. P. Collier, B. W. Wong, M. Belohradsk, F. M. Raymo, J. F. Stoddart, P. J. Kuekes, R. S. Williams, and J. R. Heath, Electronically configurable molecular-based logic gates, Science, 285:391-394, 1999; Thomas Rueckes, Kyoungha Kim, Ernesto Joselevich, Greg Y. Tseng, Chin-Li Cheung, and C. M. Lieber, Carbon nanotube-based nonvolatile random access memory for molecular computing, Science, 289:94-97, 2000; and X. Duan, Y. Huang, and C. M. Lieber, Nonvolatile memory and programmable logic from molecule-gated nanowires, Nano Letters, 2(5):487-490, 2002. The state of a switch at a crosspoint (defined by a pair of orthogonal NWs) can be sensed without changing its state by application of a smaller electric field. Such “nanocrossbars” have the potential to serve as very high density memories and programmed logic arrays (PLAs). Reference in this regard may be made to: AndréDeHon, Array-based architecture for FET-based, nanoscale electronics, IEEE Transactions on Nanotechnology, 2(1):23-32, March 2003; André DeHon, Patrick Lincoln, and John B. Savage, Stochastic assembly of sublithographic nanoscale interfaces, IEEE Transactions on Nanotechnology, 2(3):165-174, 2003; Benjamin Gojman, Eric Rachlin, and John B. Savage, Decoding of stochastically assembled nanoarrays, In Procs 2004 Int. Symp. on VLSL Lafayette, La., Feb. 19-20, 2004; Eric Rachlin, John B Savage, and Benjamin Gojman, Analysis of a mask-based nanowire decoder, In Procs 2005 Int. Symp. on VLSI, Tampa, Fla., May 11-12, 2005; and André DeHon, Seth Copen Goldstein, Philip Kuekes, and Patrick Lincoln, Nonphotolithographic nanoscale memory density prospects, IEEE Transactions on Nanotechnology, 4(2):215-228, 2005. A prototype 8×8 crossbar with a density of 6.4 Gbits/cm2 has been announced that is based on these technologies (see Yong Chen et al., Nanoscale molecular-switch crossbar circuits, Nanotechnology, 14:462-468, 2003) and a memory with storage capacity of 10 Gbits based on crossbars of NTs is promised (see http://www.nantero.com). It has been estimated that a memory density exceeding 1011 bits/cm2 is possible (André DeHon et. al., Nonphotolithographic nanoscale memory density prospects, IEEE Transactions on Nanotechnology, 4(2):215-228, 2005).
To read and store data in nanoarrays requires that individual NWs be addressable. That is, it must be possible to select one NW from each orthogonal set of NWs and apply a voltage to it or pass a current through it. To control NWs from the lithographic level requires that mesoscale wires (MWs) be used to address NWs. However, if each NW is connected to a single MW, the close packing possible with NWs is lost. Thus, schemes are needed that use multiple MWs to control individual NWs.
Several such schemes, referred to as decoders, have been proposed. All assume that MWs are placed at right angles to NWs, as suggested in FIG. 1, where the MWs are labeled Ar,i and Ac,j.
As is explained in further detail below, three types of decoders have been proposed to control MWs. Briefly, the first decoder assumes that gold particles are placed randomly between undifferentiated NWs and MWs. The second assumes that high-K dielectric regions are placed between undifferentiated lightly doped NWs (they can be controlled by electric fields) and MWs. The third assumes that NWs are differentiated during their manufacture by growing lightly doped regions into NWs (modulation doping) that have a length equal to the width of the MWs.
These three methods of addressing NWs that have been developed may be referred to as the randomized contact decoder, the mask-based decoder, and the differentiated NW decoder, respectively.
Two types of axial NW doping patterns, the (h,λA)-hot and binary reflected codes are described below. The problems that arise in controlling these NWs due to misalignment between doped and undoped NW regions and MWs are also explored. A question that arises is whether there exist fail-safe doping patterns, namely, those that guarantee that every NW is either “on” or “off”, but not in an ambiguous state as a result of misalignment.
Described now in greater detail are the conventional methods proposed for addressing differentiated and undifferentiated NWs with MWs. Each has associated with it a circuit(s), called a decoder(s), that makes one NW conductive (“turns it on”) and the rest non-conductive (“turns them off”).
The first method of addressing NWs, the randomized contact decoder, assumes that undifferentiated NWs are arranged in parallel. Gold particles are deposited at random between MWs and the NWs with the goal of placing gold particles at about half of the junctions formed by MWs and NWs (see R. S. Williams and P. J. Kuekes, Demultiplexer for a molecular wire crossbar network, U.S. Pat. No. 6,256,767, Jul. 3, 2001). The difficulty of achieving this goal has not been assessed.
Under these assumptions it has been shown that with high probability the randomized contact decoder uses 5 log2N MWs to control N NWs. That is, with this many MWs, it is possible to select an arbitrary one of N NWs to be conducting and the rest non-conducting.
The second method uses long, undifferentiated NWs. They can be grown using molecular beam epitaxy (MBE) (the SNAP method, see Nicholas A. Melosh et al., Ultrahigh-density nanowire lattices and circuits, Science, 300:112-115, Apr. 4, 2003) or by nanoimprinting (see Michael D. Austin, Haixiong Ge, Wei Wu, Mingtao Li, Zhaoning Yu, D. Wasserman, S. A. Lyon, and Stephen Y. Chou, Fabrication of 5 nm linewidth and 14 nm pitch features by nanoimprint lithography, Applied Physics Letters, 84(26):5299-5301, Jun. 28, 2004).
FIG. 3 shows a SNAP process to grow NWs by a) forming a superlattice using molecular-beam epitaxy, b) etching away alternating layers in the superlattice, c) depositing metal on the superlattice edges, and d) pressing the metals wires onto an adhesive layer of a chip.
In the SNAP method the superlattice is formed consisting of alternating layers of two materials, such as Aluminum Gallium Arsenide (AlGaAs) and Gallium Arsenide (GaAs), is formed and one type of material, such as AlGaAs, is etched back to create notches. The superlattice is turned and metal deposited on the exposed edges. The superlattice is then pressed onto a chip that contains a thin layer of an adhesive. When removed, long straight NWs are deposited. These NWs have uniform diameter and pitch, unlike the modulation-doped NWs, described below, that are assembled fluidically.
In a nano-imprinting method, a template is grown, perhaps using MBE, and the template is pressed against a soft polymer, thereby creating a contrast pattern in the polymer. Anisotropic etching removes the thin regions, thereby exposing the substrate for doping. The metallic NWs deposited by the SNAP method can also serve the same purpose. If the surface has a thin layer of Si on SiO2 which in turn is on a substrate, the SNAP metallic wires can be used with etching to expose Si NWs (see B. Johnston-Halperin et al., Fabrication of conducting silicon nanowire arrays. J. Applied Physics Letters, 96(10):5921-5923, 2004).
The method proposed to address undifferentiated NWs, referred to as the randomized mask-based decoder (see James R. Heath and Mark A. Ratner, Molecular electronics, Physics Today, 56(5):43-49, 2003), uses lithographically defined rectangular regions of low-K dielectric to shield NWs from the fields associated with MWs. As suggested in FIG. 4, if dielectric regions as small as the pitch of NWs can be produced lithographically, electric fields applied to one of ai or āi for 1≦i≦log2N, cause exactly one of N NWs to remain conducting. Here a NW separated from a MW by high-K dielectric acts as a field effect transistor (FET); the application of an electric field of the appropriate strength to the MW immobilizes carriers and drives the conductance of the NW to near zero.
FIG. 4 shows rectangular high-K and low-K dielectric regions that are interposed between vertical MWs and horizontal NWs. The low-K regions shield NWs from the effect of electric fields applied by MWs. When a field is applied to either ai or āi for 1≦4, exactly one of the 16 NWs conducts.
Because lithography puts a lower limit on the size of such regions, many randomly shifted copies of the smallest regions are used instead of the decreasingly smaller regions. The number of MWs needed to control N NWs with the mask-based decoder has been analyzed (see Eric Rachlin et al. in Procs 2005 Int. Symp. on VLSI, Tampa, Fla., May 11-12, 2005). Under very reasonable assumptions it has been shown that, as NW pitch decreases, at least 2 log2N+46 MWs will be needed. Although this number is large, the NWs grown with the SNAP process are expected to be much longer and more uniformly spaced than the modulation-doped NWs described next.
The third method, called the differentiated NW decoder, uses NWs that are grown from seed catalysts through a vapor-liquid-solid (VLS) process as depicted in FIG. 5, which shows NWs grown through a vapor-liquid-solid process that are doped as they grow. Reference in this regard can be made to Mark S. Gudiksen, Lincoln J. Lauhon, Jianfang Wang, David C. Smith, and Charles M. Lieber, Growth of nanowire superlattice structures for nanoscale photonics and electronics, Nature, 415:617-620, Feb. 7, 2002; Yiying Wu, Rong Fan, and Peidong Yang, Block-by-block growth of single-crystal Si/SiGe superlattice nanowires, Nano Letters, 2(2):83-86, 2002; and M. T. Björk, B. J. Ohlsson, T. Sass, A. I. Persson, C. Thelander, M. H. Magnusson, K. Deppert, L. R. Wallenberg, and L. Samuelson, One-dimensional steeplechase for electrons realized, Nano Letters, 2(2):87-89, 2002. In an example, silane molecules (SiH4) fall onto gold clusters, precipitating out Si atoms that solidify into crystalline silicon NWs. These NWs can be differentiated by adding dopant molecules to the gaseous mixture as they grow. NWs can be heavily and lightly doped over lengths that are determined by exposure time. This process is referred to as modulation doping when referring to the doping process, and as axial doping when referring to the result.
As stated above, when a MW is placed at right angles to a lightly doped region of a NW and separated from it by high-K dielectric, the MW and NW act as a Field Effect Transistor (FET). The doping levels are chosen so that the same field has no effect on heavily doped regions. One may say that lightly doped regions are controllable, while the heavily doped regions are uncontrollable.
Assume that each NW is given a pattern of controllable and uncontrollable regions, each of the same length. For example, two of four regions could be made controllable, as suggested in FIG. 1, where all six different doping patterns are shown.
Many axially doped NWs with the same doping profile are assembled at the same time and collected in solution. The VLS process is repeated until each of the desired doping profiles is produced. NWs are then assembled on a chip using a fluidic process. NWs with different doping profiles are mixed and floated onto the surface of a liquid where baffles align them in parallel. NWs are deposited by passing the chip up through the liquid. After drying, lithography is used to trim the NWs deposited in this manner. To produce a crossbar this procedure is applied again after turning the chip by 90 degrees. Unfortunately, this process cannot guarantee that NWs will have a uniform separation, nor can it guarantee that the boundaries of doped regions will be aligned with one another, or with any point on the chip.
When NWs are placed on a chip, insulation is used to separate the NWs from MWs that are superimposed on them. This combination of NWs and MWs forms an addressing circuit referred to as an encoded NW decoder.
As with the previously described decoders, this decoder exhibits randomness. In this case the types of NW doping pattern that fall on a chip cannot be predicted in advance. Thus, it is necessary to test the chip to discover which NW doping patterns are present. For applications that require deterministic addresses, such as memories, an auxiliary translation memory is then used to translate fixed external addresses into the particular doping patterns that are deposited on the chip during assembly. An important factor affecting manufacturability is the number of different doping patterns, C, (the size of the code space) that is needed to ensure that all or nearly all of the NWs have different doping patterns.
A discussion is now made of axial doping patterns. Two types of axial codes have been proposed, (h,λA)-hot codes (see again André DeHon, Array-based architecture for FET-based, nanoscale electronics, IEEE Transactions on Nanotechnology, 2(1):23-32, March 2003) and length λA binary reflected codes (λA-BRCs). Reference in regard to the latter can be made to Benjamin Gojman et al., Decoding of stochastically assembled nanoarrays, In Procs 2004 Int. Symp. on VLSL Lafayette, La., Feb. 19-20, 2004, and to Benjamin Gojman, Eric Rachlin, and John B. Savage, Evaluation of design strategies for stochastically assembled nanoarray memories, J. Emerg. Technol. Comput. Syst., 1(2):73-108, 2005. To describe them one may assume that controllable NW regions are aligned with MWs (see André DeHon, Patrick Lincoln, and John B. Savage, Stochastic assembly of sublithographic nanoscale interfaces, IEEE Transactions on Nanotechnology, 2(3):165-174, 2003).
FIG. 6 shows an example of modulation-doped NWs encoded with a binary reflected code of length eight.
In a (h,λA)-hot code exactly h of λA regions are controllable. To select one codeword, disabling fields are applied to (λA-h) MWs. The one codeword type whose controllable regions coincide with the MWs to which no field is applied remains conductive.
A λA-BRC has an even number of regions. The doping pattern in the first λA/2 regions is denoted by an arbitrary binary (λA/2)-tuple x (1s(0s) denote controllable (uncontrollable) regions). The doping pattern in the second λA/2 regions is denoted by the Boolean complement of x. A single λA-BRC codeword is selected by applying fields to the MWs that correspond to uncontrollable regions. The one codeword type whose controllable regions coincide with the MWs to which no field is applied remains conductive. The doping patterns for λA-BRC are a subset of the doping patterns of the (h,λA)-hot code.
More specifically, shown in FIG. 6 is an example of a binary reflected code with eight controllable or uncontrollable regions that are aligned with MWs. When the 2nd, 3rd, 5th and 8th MWs are turned on, the 1st, 5th, and 8th NWs, all of which have the same doping pattern, become activated, while all others are turned off.
Discussed now is the addressability of modulation-doped nanoarrays. Using (h,λA)-hot codes, DeHon et al. show that with high probability N modulation-doped NWs can be controlled with ┌2.2 log2N┐+11 MWs when the design goal is that all NWs doping patterns be different. Using binary reflected codes and the assumption that at least half of the NWs have different doping patterns, Gojman et al. (Decoding of stochastically assembled nanoarrays, In Procs 2004 Int. Symp. on VLSL Lafayette, La., Feb. 19-20, 2004) show that this number can be reduced to 2 log2N+8 MWs, although a somewhat better upper bound might be obtained for (h,λA)-hot codes. They also analyze the area needed for the translation memory.
With regard to the misalignment of axial codes, because fluidic assembly methods cannot control the lengthwise displacement of NWs, alignment between MWs and NW controllable regions cannot be guaranteed (see FIG. 7). To compensate for this problem, doping patterns are repeated along the length of NWs. Even with this accommodation, it remains possible that the overlap between NW controllable regions and MWs will be so small that the control of MWs cannot be definitely guaranteed. That is, a MW may be able to reduce the conductivity of a NW but not effectively turn it off. Such a NW may be said to be in an ambiguous state. The alignment problem is compounded by the difficulty of making sharp transitions between controllable and uncontrollable NW regions during the VLS manufacturing process.
To quantify the effect of misalignment, let Woverlap be the minimal length overlap needed between the field of a mesoscale wire and a NW to reduce the conductivity to a satisfactory level (see FIG. 8). In FIG. 8 the lightly shaded NW region is assumed to be controllable. When the overlap of this region and the electric field is Woverlap or less, the NW cannot be sufficiently controlled.
Let Wpitch be the pitch of MWs. Since all shifts of NWs relative to MWs are equally likely, it follows that the probability, Pcontrol, that a NW is controlled by a MW is Pcontrol=(1-2Woverlap/Wpitch), a quantity that is used below to compare NW encoding strategies.
Reference may also be made to U.S. Pat. No. 6,963,077 B2, Sublithographic Nanoscale Memory Architecture, André DeHon, Charles M. Lieber, Patrick D. Lincoln and John E. Savage, that discusses radial modulation doping of NWs in for example, columns 17-19, where the radial doping is etched away in an address window to permit an axial and radially doped NW to be addressed.